Cryptology ePrint Archive: Report 2004/215

Transitive Signatures: New Schemes and Proofs

Mihir Bellare and Gregory Neven

Abstract: We present novel realizations of the transitive signature
primitive introduced by Micali and Rivest, enlarging the
set of assumptions on which this primitive can be based, and also
providing performance improvements over existing schemes. More
specifically, we propose new schemes based on factoring, the
hardness of the one-more discrete logarithm problem, and gap
Diffie-Hellman groups. All these schemes are proven transitively
unforgeable under adaptive chosen-message attack. We also provide
an answer to an open question raised by Micali and Rivest regarding the
security of their RSA-based scheme, showing that it is transitively
unforgeable under adaptive chosen-message attack assuming the
security of RSA under one-more-inversion. We then present hash-based
modifications of the RSA, factoring and gap Diffie-Hellman based
schemes that eliminate the need for ``node certificates'' and
thereby yield shorter signatures. These modifications remain
provably secure under the same assumptions as the starting scheme,
in the random oracle model.

Publication Info: An extended abstract of this paper appeared as "Transitive Signatures based on Factoring and RSA" in Asiacrypt 2002. This is a slightly revised version of the full paper that appeared in IEEE Transactions on Information Theory, Vol.51, No. 6, pp. 2133--2151, June 2005.